So 9v isn't the way to go with this system. Got it.
Since a standard AA battery is 1500 mAh, I'm guessing some of those would be a better way to go.
I could use 4 AA to run the board.
For the heating elements, I'm going to regulate output to a constant 3.7v. Four AA will put out 4.5. Is there any advantage to adding more batteries than that into the element's circuit?